The present invention relates to calculators that are capable of being hand held and which are particularly adapted for use on board a yacht, or sailboat (the two terms are used synonymously herein), while racing.
Yacht racing is perhaps one of the most complicated racing events designed by man. In most racing events the shortest route between two points is the fastest. This is definitely not true when racing yachts. Because of the primary limitation that a yacht is incapable of sailing directly into the wind and because of such other factors as localized weather cells, currents and tides, for example, a yacht is not always capable of sailing in a straight line between two points. In fact, the course of the race to be sailed by yachts that are racing is, when physically possible, selected to maximize at least the obstacle created by the fact that a yacht cannot sail directly into the eye of the wind.
The obstacles are present for every yacht, and that is part of the challenge which makes yacht racing so absorbing. Each participant must, therefore, pit not only his or her boat handling skill but also his or her wits, knowledge and intuition against the extent to which those attributes are possessed by the competitors.
Yacht racing courses fall into three general categories--i.e., custom, selective or fixed. Custom courses are those which have a stated configuration, and the rounding marks (buoys, piers or the like which will remain in a fixed location during that race) are set to delineate the course as closely as possible to the stated configuration. In addition to setting the marks so that the actual course wil closely emulate the stated configuration, the Race Committee also considers all the wind, water and other local environmental factors to determine the proper location for each mark. Custom courses are, perhaps, the most widely employed, and specific variations are known under such names as Gold Cup, Modified Gold Cup and Olympic courses.
Selective courses are those for which the Sailing Instructions specify the location of a number of rounding marks, and prior the beginning of the race the Race Committee announces the particular marks to be employed to delineate the course for that race.
Fixed courses are those defined by marks having locations which the Sailing Instructions also delineate in specific detail. The particular marks employed to define a course are not changed prior the race, and to that extent the course is fixed, but it is possible to delineate a number of fixed courses and then select which specific fixed course is to be sailed just prior the beginning of a race.
In addition to the three, general types of yacht racing courses, there are also two, general types of races--i.e., match races and fleet races. In match races only two yachts compete in any one race. The America's Cup race exemplifies a match race.
In fleet races there are virtually any number of yachts. The yachts may all fall into a single class (wherein the yachts are identical within stated rules for that class) or the yachts may be of widely different design and therefore be sailing under an accepted "handicap" measuring system which attempts to equalize dissimilar yachts so they can race each other fairly. Normally, such handicap systems apply a mathematical factor to the actual elapsed time required for each yacht to complete the course. A corrected time is calculated when the individual factor for each yacht is applied to that yacht's elapsed time, and the results of the race are determined by comparing corrected times. The fastest corrected time, rather than the fastest elapsed time, wins the race.
The present invention has utility for yachts racing in either type race, over virtually any type of course, but at least one aspect of the invention, as will hereinafter become apparent, is primarily appropriate only to non-handicap races. To understand the present invention in the environment of any type of course, for either type of race, one need merely understand the utility of the invention for any one combination thereof. Accordinly, the invention will be described as used in conjunction with a custom course (of the Gold Cup type) in a match race between two yachts of the same class. Such a description will demonstrate all aspects of the invention.
A Gold Cup course is delineated by three marks that are located at the apices of an imaginary, preferably equilateral, triangle which is oriented with considerable particularity relative to the direction of the wind anticipated for at least the start of the race. Ideally, the race will consist of six legs sailed in the following order: (1) a first windward leg; (2) a first reaching leg; (3) a second reaching leg; (4) a second windward leg; (5) a first running, or downwind, leg; and, (6) a third windward leg. Even such a capsulated description of a Gold Cup course should make it apparent that the windward legs are particularly important inasmuch as they are sailed at least three times.
A windward leg is defined as that leg of the course which lies between the two marks located in substantial alignment with the wind direction and which requires that the yacht sail against the direction of the wind. No yacht can sail directly into the wind, because the sails will not fill, as is necessary to impart a propelling force to the yacht. However, at some angular direction relative to the wind the sails to become quite effective, and when the yacht is being so sailed it is considered as being "close hauled" or as "beating to weather." Although each yacht is somewhat different, in general, a yacht can sail effectively into the wind on a heading of approximately 45.degree. relative to the eye of the wind. By thus beating to weather along a successive series of starboard and port tacks a yacht can arrive at a point directly upwind of the starting point.
When the wind is coming over the right side of the yacht (as determined by reference to the right, or left, side of a person in the yacht who is facing the bow), and the sails are disposed, or, more nautically, "set" diagonally across the left side of the yacht, the yacht is on a starboard tack. When the wind is coming over the left side of the yacht, with the sails set across the right side of the yacht, the yacht is on a port tack.
By sailing a sequential series of starboard and port tacks a yacht will effectively move against the direction of the wind. To change from a starboard to a port tack, or vice versa, is called tacking. During the tacking maneuver, the bow of the boat passes through the eye of the wind while the sails change their disposition from one side of the yacht to the other. As the bow of the yacht heads more and more into the wind, the sails begin to luff and lose their ability to drive the boat, but if the yacht had sufficient speed at the beginning of the maneuver, and if the maneuver is carried out smoothly, the momentum of the yacht will swing the bow through the eye of the wind and beyond until the yacht is once more headed in a direction that will permit the wind to fill the sails and impart the necessary driving force to the yacht.
For a yacht which can sail most effectively into the wind at an angle of approximately 45.degree. to the wind, tacking is accomplished through an included angle of approximately 90.degree.. If such a yacht can consistently maintain its tacks through an included angle of 90.degree., or less, and does not overstand the next mark, as hereinafter more fully explained, it will likely sail the shortest total distance between the rounding marks which define the windward leg of the course being raced.
Even though race committees endeavor to set the windward mark (that rounding mark which defines the windward end of the windward leg in the course) directly to windward of the starting line, this idealized orientation is seldom accomplished. Wind shifts (a change in wind direction, often accompanied by a change in velocity) generally prevent the setting of a true windward mark. While this is not a serious problem when the windward, or weather, leg is relatively short (e.g., 1/4 to 1/2 mile), it does become significant in races incorporating a windward leg of longer than a mile, and particularly in the situation where the weather mark is not visible from the starting line. Under these circumstances, the Race Committee will post the compass headings, or directions, from the starting line to the windward mark, and from each mark to the subsequent marks of the course.
Continuing with an explanation of the windward leg, as deemed appropriate to facilitate an understanding of the present invention, for each yacht there are two imaginary lines extending from the windward, or weather, mark that are called "lay lines." The lay lines represent the paths, both starboard and port, over the water which permit a particular yacht, sailing close hauled, to fetch, and clear, the weather mark in the existing wind. As such, the lay lines are respectively parallel to the starboard and port courses of that yacht as it beats to windward. Thus, the lay lines are generally symmetrical relative to the direction of the true wind, and they diverge to leeward of the weather mark with the included angle between the lay lines being equal to the included angle through which the particular yacht can effect a tack. Inasmuch as the included angle is normally about 90.degree. one can assume that the lay lines define a right triangle when combined with extensions of the starting line.
If a yacht is sailed outside of the area bordered by the lay lines, the yacht has "overstood" the weather mark. A yacht which overstands the mark will have to travel further than one which sails within the area included between the diverging lay lines--or even along the lay lines--and the yacht which so overstands the mark will, unless sailing significantly faster, reach the weather mark after a yacht that stays within the area bounded by the lay lines. In addition to just the number of times that a yacht must traverse the windward leg during a race, the potential for exceeding the shortest distance to the windward mark when sailing the windward leg is another reason why sailing the best possible windward leg is often so important to the outcome of a yacht race.
One should not, however, fall into the trap of thinking that a yachtsman should always sail to the closest lay line, make one tack and then sail blithely to the weather mark. After all, the lay lines change their location and angular disposition in each wind shift. Over the years, therefore, yachtsmen have developed the precept of not sailing to either lay line until relatively close to the weather mark. Here again, experience is all important, and the present invention can assist even the most experienced yachtsman.
Without elaborate facilities on board the yacht to plot the course, it has heretofore been extremely difficult to determine not only what are the most advantageous headings for tacks to the windward mark but also the ratio of the distance along which, or the time on which, the yacht must sail on one tack relative to the other tack. These difficulties are compounded when one is unable to see the windward mark from the location where the race is started. Moreover, it is often virtually impossible to determine whether a competing yacht is ahead or behind when the yachts are sailing a windward leg. Certainly, when one of the two yachts finally reaches the windward mark, when the yachts cross on different tacks or when yachts are sailing side-by-side on the same tack it is possible for those sailing on either yacht to determine whether it is leading or lagging the other yacht, but by and large it is not otherwise easy for those sailing on either yacht to determine, with any reasonable degree of certainty, whether another yacht sailing a windward leg is leading or lagging.
It should be understood that on a windward leg the yachts tend to be spaced rather windely apart, as one might expect with some yachts sailing on starboard tack and others sailing on port tack. When yachts are sailing on divergent tacks, they are sailing away from each other on headings that are generally perpendicular to each other. This tends to separate yachts sailing the windward leg, and inasmuch as the wind itself is never identical in either strength or direction at all locations across the surface of the water on which the race is being held a distant yacht may be gaining a definite advantage that may not be readily ascertained. For that reason each yachtsman desires to maintain a continuous assessment as to whether he is leading or lagging the competitors. If, for example, a yachtsman is aware that a competitor at a distant location is gaining, or moving ahead, it may be wise for the yachtsman to sail toward the competitor in an attempt to obtain the benefit of the more favorable wind conditions that appear to be present in proximity to the competitors location. Economical means for providing such information has not heretofore been readily available.
The above described difficulties in determining the relative position of competing yachts from aboard one of those yachts does not exist on those legs of a course other than the windward leg. On the other legs the yachts generally proceed along substantially a straight line between the marks defining those legs so that relative position can be readily ascertained simply by noting relative position.